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Discrete Structures:
Course Notes
Mike Janssen
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Front Matter
1
Logic
1.1
Introduction to Mathematical Statements
1.2
Logical Connectives and Equivalence
1.2.1
Logical Connectives
1.2.2
Logical Equivalence
1.3
Quantifiers
2
Introduction to Graphs
2.1
Toward a Definition of a Graph
2.1.1
Worksheet
3
Proof Techniques
3.1
Direct Proof
3.1.1
Exploring Graphs
3.2
Proof by Contradiction
3.3
Proof via Contrapositive (And Other Methods)
3.3.1
Proof via the Contrapositive
3.3.2
Proofs with Cases, and Biconditional Proofs
3.4
Induction
4
Set Theory
4.1
The idea of a set
4.1.1
Describing Sets
4.1.2
Subsets and Set Equality
4.1.3
Cardinality
4.2
Operations with Sets
4.2.1
Union, Intersection, and Equality of Sets
4.2.2
Complement and Difference
4.2.3
Cartesian Products
4.3
Families of Sets
4.4
Using sets to describe graphs
4.4.1
Worksheet
5
Relations and Functions
5.1
Relations
5.1
Worksheet
5.2
Functions
5.2.1
Worksheet
5.3
Properties of Functions
5.3.1
Worksheet
6
Further Explorations in Graph Theory
6.1
Trees
6.1.1
Worksheet
6.2
Graph Coloring
6.2.1
Worksheet
6.2.1.1
Vertex Coloring
6.2.2
Worksheet
6.2.2.1
Edge Coloring
7
Infinity
7.1
Infinite Cardinality
7.1.1
The Cantor-Schroeder-Bernstein Theorem
7.2
Uncountable Sets
Backmatter
A
On Mathematical Writing
Index
Colophon
Colophon
Colophon
This book was authored in PreTeXt.